Modification of Plasma Solitons by Resonant Particles

Karpman, V. I.; Lynov, Jens-Peter; Michelsen, Poul; Pécseli, H. L.; Rasmussen, Jens Juul; Turikov, V. A.

doi:10.1103/physrevlett.43.210

Cited by 29 publications

(16 citation statements)

References 8 publications

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“…However, strictly speaking, this is inconsistent with the boundary conditions at infinity, ∣ x ∣ = ∞, as the unperturbed distribution f i 0 does not satisfy this requirement in the general case. Actually, the reflected particles are responsible for a collisionless damping of the soliton [ Ott and Sudan , 1970; Krivoruchko et al , 1975; Karpman et al , 1980], so that the stationary BGK approach loses its meaning. Nevertheless, we can ignore the damping provided the reflected ion population is negligibly small.…”

Section: Positive Solitary Bgk Pulsementioning

confidence: 99%

Electrostatic solitary waves as collective charges in a magnetospheric plasma: Physical structure and properties of Bernstein–Greene–Kruskal (BGK) solitons

2003

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[1] The electrostatic pulses recorded by the Geotail spacecraft and labeled electrostatic solitary waves (ESW) are considered within the framework of Bernstein-Greene-Kruskal (BGK) solitons. The main goal of this paper is to develop sufficiently general and simple theoretical models of the nonlinear wave perturbations under study. Such models are necessary for understanding the physical structure and properties of the observed waves as well as for the treatment of the extensive experimental material, which has been accumulated on the ESW waveforms and for meaningful data processing. Examples of localized BGK modes described previously in literature are difficult to compare with the experimental data due to their particular nature. In contrast to these particular models, the general approach developed in the article applies to arbitrary particle distributions of the background plasma, velocities of the BGK solitons and wide variety of the recorded ESW waveforms. Relying on the theory of BGK solitons, with an emphasis on their general properties, the work contains a consistent analytical description and physical interpretation of ESW as effective spatial charges shielded by a collisionless plasma. The general analysis of localized BGK waves leads to a number of new results, such as unified physical models of ESW based on the additivity of the distribution function, as well as energetic relations and universal restrictions on the parameters and waveforms of the solitons. The new models and physical interrelations reveal universal features of the BGK soliton structure and allow a direct juxtaposition with the observations. The established interconnections between the physical characteristics of the waves agree well with the Geotail data on ESW waveforms. We also discuss less studied nonstationary phenomena, among which are wave emission by the BGK solitons, mechanisms of electron phase density hole interaction and certain questions of stability. Some of the most typical examples of the various BGK solutions described in the article are useful for a correlation between the theory and measurements as well as for an identification of the ESW waveforms observed in the magnetosphere.

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Section: Positive Solitary Bgk Pulsementioning

confidence: 99%

Electrostatic solitary waves as collective charges in a magnetospheric plasma: Physical structure and properties of Bernstein–Greene–Kruskal (BGK) solitons

2003

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“…We feel that such solution will be useful in a manifold similar physical situations. 27,28 The nonlinear, time-dependent solutions for EACW oscillations involving dispersive and nonlinear effects are self contained and hope to improve our understanding to study nonlinear phenomena in the frontier of modern physics and technology.…”

Section: Discussion and Summarymentioning

confidence: 99%

Nonlinear electron acoustic cyclotron waves in presence of uniform magnetic field

et al. 2013

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Nonlinear electron acoustic cyclotron waves (EACW) are studied in a quasineutral plasma in presence of uniform magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary charge neutral inhomogeneous background. In long wavelength limit, it is shown that the linear electron acoustic wave is modified by the uniform magnetic field similar to that of electrostatic ion cyclotron wave. Nonlinear equations for these waves are solved by using Lagrangian variables. Results show that the spatial solitary wave-like structures are formed due to nonlinearities and dispersions. These structures transiently grow to larger amplitude unless dispersive effect is actively operative and able to arrest this growth. We have found that the wave dispersion originated from the equilibrium inhomogeneity through collective effect and is responsible for spatiotemporal structures. Weak dispersion is not able to stop the wave collapse and singular structures of EACW are formed. Relevance of the results in the context of laboratory and space plasmas is discussed. V C 2013 American Institute of Physics.

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“…Further motivation for studying the stability properties of the fifth-order nonlinear dispersive equations comes from the result of the recent study on the role of the fifth-order dispersion term on the soliton stability of the usual KdV type linear dispersion equations. For example, it has been shown that [5] the solitary wave solutions of the fifth-order equation of the type…”

Section: Introductionmentioning

confidence: 99%

“…are unstable with respect to the collapse type instabilities, if p ≥ 4 for β =0 while for β = 0, i.e. the addition of the fifth-order term stabilizes the soliton for p>4 [5]. The exact upper limit of the nonlinearity parameter p in this case is still an open question [6].…”

Section: Introductionmentioning

confidence: 99%

Stability of compacton solutions of fifth-order nonlinear dispersive equations

Dey

Khare

2000

J. Phys. A: Math. Gen.

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We consider fifth-order nonlinear dispersive K(m, n, p) type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons -the compact solitary waves free of exponential tails. This interaction also generates many other solitary wave structures like cuspons, peakons, tipons etc. which are otherwise unattainable with linear dispersion. Various self similar solutions of these higher order nonlinear dispersive equations are also obtained using similarity transformations. Further, it is shown that, like the third-order nonlinear K(m, n) equations, the fifth-order nonlinear dispersive equations also have the same four conserved quantities and further even any arbitrary odd order nonlinear dispersive K(m, n, p...) type equations also have the same three (and most likely the four) conserved quantities. Finally, the stability of the compacton solutions for the fifth-order nonlinear dispersive equations are studied using linear stability analysis. From the results of the linear stability analysis it follows that, unlike solitons, all the allowed compacton solutions are stable, since the stability conditions are satisfied for arbitrary values of the nonlinear parameters.

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Modification of Plasma Solitons by Resonant Particles

Cited by 29 publications

References 8 publications

Electrostatic solitary waves as collective charges in a magnetospheric plasma: Physical structure and properties of Bernstein–Greene–Kruskal (BGK) solitons

Electrostatic solitary waves as collective charges in a magnetospheric plasma: Physical structure and properties of Bernstein–Greene–Kruskal (BGK) solitons

Nonlinear electron acoustic cyclotron waves in presence of uniform magnetic field

Stability of compacton solutions of fifth-order nonlinear dispersive equations

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